Use of stochastic models to estimate the growth of the Port Jackson shark, Heterodontus portusjacksoni, off eastern Victoria, Australia

Abstract

Three stochastic models were used to describe the growth of Heterodontus portusjacksoni off eastern Victoria, Australia. The models are based on a reparametrization of the von Bertalanffy growth model to take account of length-at-age heterogeneity, and incorporate random variation of the von Bertalanffy growth coefficient ( k), using three different probability distribution functions ( pdfs): Weibull, gamma and log-normal. They were fitted to the lengths of 179 specimens (79 females and 100 males), and associated age estimates obtained by counting growth bands in the inner trunk dentine layer of the dorsal-fin spines. The species is relatively long-lived (maximum estimated age of 35 years for females and 28 years for males) and slow growing, but has rapid growth during the early stages of life. All the models provided similar growth parameters and length-at-age quantiles. However, Kullbacḱs information mean indicated that the stochastic model assuming a log-normal distribution fitted the length-at-age data better for both females ( L∞ = 1337, E( k) = 0.059, t 0 = 5.294) and males ( L∞ = 1125, E( k) = 0.075, t 0 = 4.944) than the models assuming other distributions. The χ 2 likelihood ratio test indicated that females and males grow differently.